Tuesday, 15 December 2015

Does Zero Exist?

One of the greatest attributes of enquiry-based learning is how a student's wondering can lead us all to a fascinating learning journey.We had been theorising which number was the base for our number system ( Link: Why is our number system the way it is? ) when one student wondered if it was zero..........We thought about this idea and are wonderings grew.One student then theorised that it cannot be, because zero is just nothing.Is it?We shared our theories about this and how we could explain what zero was. Some fascinating ideas emerged.I then shared how to this day no mathematician nor scientist in history has been able to prove or disprove the existence of zero.- But how can that be?- If we use zero, surely someone must know what it actually is?I then remarked that if you were able to prove or disprove the existence of zero, you would likely receive a Nobel Peace Prize and become one of the world's most famous mathematicians and scientist. - Wow! Really??????- Why?- Let's do it! Someone excitedly suggested we should group together and see if we can prove it. Such a great idea and enthusiastically they grouped and thought deeply. The discussions were rich with creating hypotheses and testing each other's philosophies. We then shared some of our thinking:

I was completely blown away by the thinking being generated!!I particularly liked how one student proved their theory by drawing the symbol for zero and explaining how there is nothing inside it. And though it sounds rather simplistic, the thought shared that 'It is the whole of everything' gets more and more profound the more you think about it.Some thought how Roman numerals didn't have a zero. Oh! So it must be a NEW number! Wow! But, is it a number?

We discussed that every number CAN be proven. We can prove 2 exists because 2 is 2 ones OR 1 split in half to create 2. Every number therefore CAN be proven, but zero? How can we prove nothing exists? And where did 1 come from? How can 1 come from nothing?!?!?Someone then connected that's like the Big Bang theory - everything in the universe came from nothing suddenly! Wow! Others then sparked from this connection and suggested zero could be like a black hole. Another thought zero is like God who must have come from nothing because He created everything. Woah.....talk about deep thinking (and bare in mind these are 10 year olds coming up with these amazing thoughts!)Someone then mentioned zero can be proven because I am a 1. I am a 1 person and when I die, I don't exist anymore so that is like zero. But does our body really stop existing we wondered? When it decomposes it just changes into different smaller materials so the body hasn't realély ever stopped existing, it just changes it's existence! Again - 10 year olds thinking like this!!! Amazing!As the bell rang for recess it was suggested we try to keep thinking about this next week and the week after. Wow! Love this so much!! Totally engaged, really passionate and directing / taking ownership of what we should be doing in our classroom- brilliant!To keep this fresh in our minds to keep thinking about, here is how our classroom door looks now as we enter:

Later in the day, after lunch, a student came in with her note book sharing that she might have cracked the existence of zero. She figured that 1 + 1 = 2. Therefore 1 - 1 = 0.She thought about positive 1 and negative 1 and that if the zero place wasn't there the positive 1 and the negative 1 would be arguing for that prime position of zero. Does that beginning thinking help us to prove zero exists? I'm not sure, but what I do know is that she is really thinking deeply about place value and the thoughts the students generated as a whole class, individually and in pairs about our place value system could not occur had this been a worksheet place value activity.

Who says 10 year olds can't have deep philosophical discussions about maths?